Question: What is Standard Index Form ?


6.472 146308
When the result of a calculation with a calculator goes beyond the size of the calculator's display it is presented in standard form. For example, the above result was recorded from a calculator's display after calculating 8653
This has to be interpreted as 6.472 146 3 x 108 which equals 647 214 630.

A number is expressed in standard form when it is given as a number with one non-zero digit to the left of the decimal point multiplied by a power of 10. All numbers can be expressed in this way. For example,

329 = 3.29 x 102
46 700 = 4.67 x 104
0.0071 = 7.1 x 10-3

The power of 10 required can be found by noting how many places the decimal point has to be moved to the left or right to obtain a number with one non-zero digit to its left.
For example,
870 235.0 = 8.702 35 x 105
0.000 276 = 2.76 x 10-4

Standard form is particularly useful in dealing with very large or very small numbers as needed in science and astronomy.
For example :

  • A molecule of water has a mass of 2.99 x 10-26 kg;
  • The mass of the moon is 7.37 x 1022